It was a grim display by the Gunners but they did just enough to grab the point they needed to cement their place at the top of Group H.
Arsene Wenger opted to rest most of his first-team regulars with Cesc Fabregas, Kolo Toure, Tomas Rosicky and Alexander Hleb all left at home.
Wenger's starting line-up was virtually a second team but it was understandable considering the north London side had won all three of their group games without conceding a goal.
Despite being hammered by Arsenal last month, Slavia could not be under-estimated as Karel Jarlom's side lead the Czech league by six points after 12 games of the season and beat Teplice 1-0 on Saturday.
Slavia started the match very cagily, almost as though they were the away team, and seemed in awe of what was essentially Arsenal's second-string side.
However, they did create the first opening of a very dull first period in the 14th minute when, from the first corner of the match, an unmarked Mickael Tavares headed an excellent chance over the bar.
The incident seemed to lift Slavia as they started to pass the ball more confidently and, in the 36th minute, Zdenek Senkerik made room for himself inside the area before forcing Manuel Almunia to make a fingertip save.
While Arsenal struggled to get any momentum going, Slavia created another great move on the stroke of half-time that ended with Senkerik heading over the bar, although the striker was flagged offside.
The heavens opened in Prague at the break and the second half was played in torrential rain as Arsenal looked to extend their 25-game unbeaten run in all competitions.
Slavia thought they should have had a penalty in the 50th minute when Senkerik was bundled over in the area but the referee waved play on.
Arsenal were marginally better in the second half but the woeful Eduardo and dire Theo Walcott failed to create any openings.
Slavia continued to look the likelier side to break the deadlock and, with 20 minutes left, Frantisek Drizdal's superb run and cross caused chaos in the Gunners defence until Alexandre Song eventually cleared the ball.
The best chance of the game came in the 76th minute when Senkerik latched on to a long ball and tried to lift his shot over Almunia only for the keeper to make a solid save.
With five minutes left, substitute Emmanuel Adeyabor's header was easily gathered by Michal Vorel - the first and only time the Slavia keeper was forced to make a save.
It was job done for Arsenal though, as they qualified for the knockout stages of the competition with two rounds of group games still to go.